MANOVA is used to examine the differences between independent variable and more than one continuous dependent variable. Also it is a test statistic that cannot tell you which specific variables are significantly different of each other. As far you have more than two DV, which are continious, Manova could help you just in the case of finding significance differences.

I recommend to find nonlinear relationship among your variables.

I would recommend the MANOVA approach as it considers more information assuming you have sufficient sample size. If you used repeated ANOVAs, it would ignore the interrelationships among the DVs that might help explain your result as well as expand your Type I Error Rate. You could always use ANOVAs as a follow up to a significant MANOVA. If you use MANOVA, be sure to use the Canonical Relationships to help explain your results.

Thank you for your answers.

I do not really understand what you mean by find non-linear relationships among my variables, and by the use of canonical relationships to explain my results. Can you explain what you mean?

Indeed, my sample size for MANOVA can be a problem. I have unequal sample size group and for some of them, there are only 10 participants. I read somewhere that MANOVA need more participants by group than number of IV, but I also read something else. Do you think that is OK to run MANOVA with 3 IV, 5 DV, with a minimum of 10 participant by group and a maximum of 20?

I did not mean to suggest "non" linear relationships. Only that the MANOVA takes into account the relationships among the variables as well as the differences. Multiple ANOVAs will only look at differences among the IVs. Based on your sample sizes, you would have a problem running a MANOVA. Looking at the canonical relationships between your IVs and DVs gives you added information on not only the differences, but the nature of the relationships. While the different group sample sizes are not a problem, the small sample sizes would give your analysis very little power. Even with the multiple ANOVAs, your analyses will need rather large differences to be significant.

Considering the problem of sample size for MANOVA, I think (I hope) I can compute a mixed factorial ANOVA with 2 repeated measures (air of interest and sub-period) even if the statistical power will be lower than a bigger sample size... I will not have informations about the combination of DVs, but on the other hand, this analysis will show if there are differences between each air of interest.

Thank you for your answers.